grades
student_1 85
student_2 90
student_3 75
student_4 86
student_5 91
Descriptive statistics that offer information on where the scores in a data set tend to cluster.
Examples: Mean, Median, Mode.
image: Corporate Finance Institute
The arithmetic average of a variable within a set of data.
\[\bar{x} = \frac{\sum x}{n}\]
\(\bar{x}\) = Mean
\(\sum\) = Summation
\(x\) = Values in a column
\(n\) = Sample size
We have five college student’s test scores on a particular exam:
grades
student_1 85
student_2 90
student_3 75
student_4 86
student_5 91
\[\bar{x} = \frac{(85 + 90 + 75 + 86 +91)}{5}\]
\[\bar{x} = ?\]
A score that cuts a distribution in half, or more simply, the true middle number.
Steps to Find the Median
We only need one step for this!
\[Median = \frac {n + 1}{2} \]
\(n\) = Sample size
LM and UM are numbers within the column.
Step 1
\[Lower Middle (LM) = \frac {n}{2} \]
Step 2
\[Upper Middle (UM) = \frac {n}{2} +1 \]
Step 3
\[Median = \frac {LM + UM}{2}\]
We have nine college student’s test scores on a particular exam:
grades
student_1 85
student_2 90
student_3 75
student_4 86
student_5 62
student_6 79
student_7 96
\[Median = \frac {? + 1}{2} \]
We have four college student’s test scores on a particular exam:
grades
student_1 85
student_2 90
student_3 75
student_4 86
\[(LM) = \frac {?}{2} \] \[(UM) = \frac {?}{2} +1 \] \[ Median = \frac {(? + ?)}{2}\]
The most frequent number in a set of scores or column.
Simply sort your values in ascending order, then count and compare (Hint: Look for numbers that repeat).
image: wikiHow
We have seven college student’s test scores on a particular exam:
grades
student_1 85
student_2 90
student_3 75
student_4 85
student_5 62
student_6 79
student_7 96
\[ Mode = ?\]
A set of scores that cluster in the center and tapers off to the left and right sides of the number line.
Extreme values that pull the distribution which leads to a positive or negative skew.
image: Medium
A clustering of scores in a distribution with some large scores pulled (or skewed) toward the positive side of the x-axis
A clustering of scores in a distribution with some small scores that pulled (or skewed)the towards the negative side of the x-axis.
These are memory techniques that aid in memory retention and retrieval.
Dates back to the early Greeks.
Helps transition short term to long term memory more quickly.
image: ShowMe
When you hear the word “skew” think of laying on a beach and putting your feet together while looking at the horizon.
Your right foot is the positive skew.
Your left foot in the negative skew.
image: Michael Britt
Using the data below, calculate the mean, median, and mode.
Wins_Under_Scott_Frost
2018 4
2019 5
2020 3
2021 3
2022 4
Mean = ?
Median = ?
Mode = ?
01:00
Right skew occurs when our Mean > Median.
Left skew occurs when our Mean < Median.
Image: Emory University
The deviation score is the distance between the mean of a variable and any given raw score in that variable.
\[d_i = x_i - \bar{x}\]
\(d_i\) = deviation score
\(x_i\) = a given raw score (i.e., data point)
\(\bar{x}\) = the mean
This tells us two important things:
1.) How far the raw score is from the mean (\(\bar{x}\))
2.) Whether the raw score is greater or less than the mean (\(\bar{x}\))
Positive deviation scores represent raw scores that greater than the mean.
Negative deviation scores represent raw scores that less than the mean.
1.) Calculate the (\(\bar{x}\))
2.) Calculate the \(d_i = x_i - \bar{x}\) for each student
grades
student_1 85
student_2 90
student_3 75
student_4 85
student_5 62
student_6 79
student_7 96
You are a researcher at a think tank and you are about to present new findings regarding the DARE program. Your data has a (\(\bar{x}\)) of 45, a median that is 35, what type of skew will your sample have? And what direction does it point?
A.) Positive Skew, Right
B.) Positive Skew, Left
C.) Negative Skew, Left
D.) Positive Skew, Right
01:00
Any question about the exam?
Bring a calculator.
Giphy